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Consider the graph of $g(x)$ shown below.

Which statement about $g(x)$ is NOT true?

$g(x)$ is continuous but not differentiable at $x=a$

$\lim \limits_{x \to a^+} \cfrac{g(x)-g(a)}{x-a} \neq \lim \limits_{x \to a^-} \cfrac{g(x)-g(a)}{x-a}$

$\lim \limits_{h \to 0} \cfrac{g(b+h)-g(b)}{h}=0$

$g’(x)$ exists at $x=c$